Abstract

Neuronal synchronization plays an important role in the various functionality of nervous system such as binding, cognition, information processing, and computation. In this paper, we investigated how random and intentional failures in the nodes of a network influence its phase synchronization properties. We considered both artificially constructed networks using models such as preferential attachment, Watts-Strogatz, and Erdős-Rényi as well as a number of real neuronal networks. The failure strategy was either random or intentional based on properties of the nodes such as degree, clustering coefficient, betweenness centrality, and vulnerability. Hindmarsh-Rose model was considered as the mathematical model for the individual neurons, and the phase synchronization of the spike trains was monitored as a function of the percentage/number of removed nodes. The numerical simulations were supplemented by considering coupled non-identical Kuramoto oscillators. Failures based on the clustering coefficient, i.e., removing the nodes with high values of the clustering coefficient, had the least effect on the spike synchrony in all of the networks. This was followed by errors where the nodes were removed randomly. However, the behavior of the other three attack strategies was not uniform across the networks, and different strategies were the most influential in different network structure.

Received 11 June 2011Accepted 12 August 2011Published online 23 September 2011

Lead Paragraph: Neural networks are the prototypic examples of complex networks where populations of individual neurons interact through a complex coupling configuration. Synchronization, which is thought to be a major responsible for binding in neural systems, is the most frequent collective behavior observed in dynamical networks. It is linked to various brain functions and many of the brain disorders have been shown to alter the synchronization level in the brain. Neural networks, like other type of complex networks, might undergo failures in their components, and as a consequence, lose proper functioning. These failures can be random or targeted. In this work, we investigated how random and targeted failures in the nodes influence the phase synchronization in a network of interacting Hindmarsh-Rose neurons.

Acknowledgments:

The author would like to thank Homa Babai for assistance in the preparation of the manuscript.